Journal
INTERNATIONAL JOURNAL OF MATHEMATICS
Volume 25, Issue 9, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129167X14500815
Keywords
C*-tensor categories; special unitary group; twistings; Hecke algebras
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Funding
- European Research Council under the European Unions [307663]
- European Research Council (ERC) [307663] Funding Source: European Research Council (ERC)
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Kazhdan and Wenzl classified all rigid tensor categories with fusion ring isomorphic to the fusion ring of the group SU(d). In this paper we consider the C*-analogue of this problem. Given a rigid C*-tensor category C with fusion ring isomorphic to the fusion ring of the group SU(d), we can extract a constant q from C such that there exists a *-representation of the Hecke algebra H-n(q) into C. The categorical trace on C induces a Markov trace on H-n(q). Using this Markov trace and a representation of H-n(q) in Rep(SU (root q)(d)) we show that C is equivalent to a twist of the category Rep(SU (root q)(d)). Furthermore a sufficient condition on a C*-tensor category C is given for existence of an embedding of a twist of Rep(SU (root q)(d)) in C.
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